An improved model of alliances between political parties

TL;DR

This paper develops an extended operatorial model of political party alliances that includes interactions with electors and undecided voters, making it more realistic and solvable through quadratic Hamiltonians.

Contribution

It introduces a new model incorporating interactions with electors and undecided voters, extending previous models for better realism and solvability.

Findings

Explicit solutions for decision functions in specific scenarios

Model closer to real political dynamics

Extension of previous models to include more interactions

Abstract

We consider an operatorial model of alliances between three political parties which interact with their electors, with the undecided voters, and with the electors of the other parties. This extends what was done in a previous paper, where this last type of interactions was not considered. Of course, taking them into account makes the system closer to real life. To produce an exactly solvable model, we restrict here to quadratic Hamiltonians, so that the equations of motion turn out to be linear. The dynamics of the so-called {\em decision functions} are deduced, and some explicit situations are considered in details.